Controllability of consensus heterogeneous multi-agent networks over continuous time scale

• Autorzy: Athira V. S. , Muni Vijayakumar S. , Rafeek Kallu Vetty Muhammed , Reddy Gudala Janardhana

Identyfikatory

DOI

10.2478/candc-2023-0037

• Języki publikacji: EN

Abstrakty

EN

The research, presented in this paper, concernes the controllability of a multi-agent network with a directed, unweighted, cooperative, and time-invariant communication topology. The network’s agents follow linear and heterogeneous dynamics, encompassing first-order, second-order, and third-order differential equations over continuous time. Two classes of neighbour-based linear distributed control protocols are considered: the first one utilises average feedback from relative velocities/relative accelerations, and the second one utilises feedback from absolute velocities/absolute accelerations. Under both protocols, the network’s agents achieve consensus in their states asymptotically. We observe that both of the considered dynamical rules exploit the random-walk normalised Laplacian matrix of the network’s graph. By categorising the agents of the network into leaders and followers, with leaders serving as exogenous control inputs, we analyse the controllability of followers within their state space through the influence of leaders. Specifically, matrix-rank conditions are established to evaluate the leader-follower controllability of the network under both control protocols. These matrix-rank conditions are further refined in terms of the system matrices’ eigenvalues and eigenvectors. The inference diagrams presented in this work provide deeper insights into how leader-follower interactions impact the network controllability. The efficacy of the theoretical findings is validated through numerical examples.

Słowa kluczowe

EN

multi-agent systems; controllability; heterogeneous; agent models

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2023
• Tom: Vol. 52, No. 2
• Strony: 199--245
• Opis fizyczny: Bibliogr. 34 poz.

Twórcy

autor

Athira V. S.

• Department of Mathematics, Central University of Karnataka, Kadaganchi P. O., Kalaburagi District 585367, India

autor

Muni Vijayakumar S.

• Department of Mathematics, Smt. Indira Gandhi Government First Grade Women’s College, Sagara P. O., Shivamogga District 577401, India

autor

Rafeek Kallu Vetty Muhammed

• Department of Mathematics, Central University of Karnataka, Kadaganchi P. O., Kalaburagi District 585367, India

autor

Reddy Gudala Janardhana

• Department of Mathematics, Central University of Karnataka, Kadaganchi P. O., Kalaburagi District 585367, India

Bibliografia

• ALDOUS, D. (1991) Applications of random walks on finite graphs. IMS Lecture Notes-Monograph Series 18, 12–26. DOI: https://www.jstor.org/stable/4355644
• BONDY, J. A. and MURTY, U. S. R. (2008) Graph Theory. Springer-Verlag, London.
• CHEN, F. and REN, W. (2019) On the control of multi-agent systems: A survey. Foundations and Trends in Systems and Control 6 (4), 339–499. DOI: https://doi.org/10.1561/2600000019
• COPPERSMITH, D., DOYLE, P., RAGHAVAN, P. and SNIR, M. (1993) Random walks on weighted graphs and applications to on-line algorithms. Journal of the ACM 40 (3), 421–453. DOI: https://doi.org/10.1145/174130.17413110.1145/174130.174131
• DEFOORT, M., POLYAKOV A., DEMESURE, G., DJEMAI, M. and VELUVOLU, K. (2015) Leader–follower fixed-time consensus for multi-agent systems with unknown non-linear inherent dynamics. IET Control Theory & Applications 9 (14), 2165–2170. DOI: https://doi.org/10.1049/ietcta.2014.1301
• FRIEDBERG, S. H., INSEL, A. J. and SPENCE, L. W. (1989) Linear Algebra. Prentice Hall, New Jersey.
• GENG, H., WU, H., MIAO, J., HOU, S. and CHEN, Z. (2022) Consensus of heterogeneous multi-agent systems under directed topology. IEEE Access 10, 5936–5943. DOI: https://doi.org/10.1109/ACCESS.2022.3142539
• GREGUŠ , M. (1987) Third Order Linear Differential Equations. D. Reidel Publishing Company, Dordrecht.
• GUAN, Y., JI, Z., ZHANG, L. and WANG, L. (2016) Controllability of heterogeneous multi-agent systems under directed and weighted topology. International Journal of Control 89 (5), 1009–1024. DOI: https://doi.org/10.1080/00207179.2015.1110756
• JAYARAMAN, G., PADMANABHAN, N. and MEHROTRA, R. (1986) Entry flow into a circular tube of slowly varying cross section. Fluid Dynamics Research 1 (2), 131–144. DOI: https://doi.org/10.1016/0169-5983(86)90013-4
• KURRAS, S. (2016) Variants of the Graph Laplacian with Applications in Machine Learning. Ph.D. dissertation. Universität Hamburg, Hamburg.
• LELEUX, P., COURTAIN, S., FRANCOISSE, K. and SAERENS, M. (2022) Design of biased random walks on a graph with application to collaborative recommendation. Physica A: Statistical Mechanics and its Applications 590, 126752. DOI: https://doi.org/10.1016/j.physa.2021.126752
• LIU, J., AN, B. and WU, H. (2018) Consensus of third-order multi-agent systems with communication delay. 2018 Chinese Control And Decision Conference, 1428–1432. DOI: https://doi.org/10.1109/CCDC.2018.8407351
• LIU, Y.-Y. and BARAB´ ASI, A.-L. (2016) Control principles of complex systems. Reviews of Modern Physics 88 (3), 035006. DOI: https://doi.org/10.1103/RevModPhys.88.035006
• LIU, B., CHU, T., WANG, L. and XIE, G. (2008) Controllability of a leader–follower dynamic network with switching topology. IEEE Transactions on Automatic Control 53 (4), 1009–1013. DOI: https://doi.org/10.1109/TAC.2008.919548
• LIU, K., XIE, G. and WANG, L. (2012) Consensus for multi-agent systems under double integrator dynamics with time-varying communication delays. International Journal of Robust and Nonlinear Control 22 (17), 1881–1898. DOI: https://doi.org/10.1002/rnc.1792
• LOZANO, R., SPONG, M. W., GUERRERO, J. A. and CHOPRA, N. (2008) Controllability and observability of leader-based multi-agent systems. 47th IEEE Conference on Decision and Control, 3713–3718. DOI: https://doi. org/10.1109/CDC.2008.4739071
• MESBAHI, M. and EGERSTEDT, M. (2010) Graph Theoretic Methods in Multiagent Networks. Princeton University Press, Princeton.
• MUNI, V. S., RAFEEK, K. V. M., ATHIRA, V. S. and REDDY, G. J. (2023) Controllability of consensus of multi-agent networks over heterogeneous dynamics. Results in Control and Optimization 12, 100272. DOI: https://doi.org/10.1016/j.rico.2023.100272
• MUNI, V. S., RAFEEK, K. V. M., REDDY, G. J. and GEORGE, R. K. (2022) On the selection of leaders for the controllability of multi-agent networks. Bulletin of the Iranian Mathematical Society 48 (6), 3141–3183. DOI: https://doi.org/10.1007/s41980-022-00683-2
• PADHI, S. and PATI, S. (2014) Theory of Third-Order Differential Equations. Springer, New Delhi.
• REN, W. (2007) Consensus strategies for cooperative control of vehicle formations. IET Control Theory & Applications 1 (2), 505–512. DOI: https://doi.org/10.1049/iet-cta:20050401
• REN, W. and BEARD, R. W. (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control 50 (5), 655–661. DOI: https://doi.org/10.1109/TAC. 2005.846556
• REYNOLDS, D. W. (1989) Bifurcation of harmonic solutions of an integrodifferential equation modelling resonant sloshing. SIAM Journal of Applied Mathematics 49 (2), 362–372. DOI: https://doi.org/10.1137/01490 22
• SABER, R. O. and MURRAY, R. M. (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49 (9), 1520–1533. DOI: https://doi.org/10.1109/TAC. 2004.834113
• TANNER, H. G. (2004) On the controllability of nearest neighbour interconnections. 43rd IEEE Conference on Decision and Control, 2467–2472. DOI: https://doi.org/10.1109/CDC.2004.1428782
• TERRELL, W. J. (2009) Stability and Stabilization: An Introduction. Princeton University Press, Princeton.
• XIE, D., YUAN, D., LU, J. and ZHANG, Y. (2013) Consensus control of second-order leader–follower multi-agent systems with event-triggered strategy. Transactions of the Institute of Measurement and Control 35 (4), 426–436. DOI: https://doi.org/10.1177/0142331212454046
• YAZICIOĞLU, A. Y. and EGERSTEDT, M. (2013) Leader selection and network assembly for controllability of leader–follower networks. American Control Conference, 3802–3807. DOI: https://doi.org/10.1109/ACC.2013. 6580419
• YU, W., REN, W., ZHENG, W. X., Chen, G. and LÜ, J. (2013) Distributed control gains design for consensus in multi-agent systems with secondorder nonlinear dynamics. Automatica 49 (7), 2107–2115. DOI: https:// doi.org/10.1016/j.automatica.2013.03.005
• ZHANG, L., SUN, J. and YANG, Q. (2021) Distributed model-based eventtriggered leader–follower consensus control for linear continuous-time multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems 51 (10), 6457–6465. DOI: https://doi.org/10.1109/TSMC.2019. 2962735
• ZHENG, Y. and WANG, L. (2012) Finite-time consensus of heterogeneous multi-agent systems with and without velocity measurements. Systems & Control Letters 61 (8), 871–878. DOI: https://doi.org/10.1016/j.sysconle. 2012.05.009
• ZHENG, Y. and WANG, L. (2012) Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. International Journal of Control 85 (12), 1967–1976. DOI: https://doi.org/10.1080/0020 7179.2012.713986
• ZHENG, Y., ZHU, Y. and WANG, L. (2011) Consensus of heterogeneous multiagent systems. IET Control Theory & Applications 5 (16), 1881–1888. DOI: https://doi.org/10.1049/iet-cta.2011.0033